I'm planning a trip and one of my main points is not to fly unless absolutely necessary. My biggest problem is how to cross from Asia to America without a plane. If it's absolutely impossible to cross the Bering Strait without flying, which is the shortest route? Maybe a small airplane?
Crossing Bering Strait on a boat does seem possible but it's going to be difficult practically. Adam Katz put together a bunch of notes on how to do this. From the looks of it, it appears you might have to pay your way through it on commercial fishing vessels which operate in the area.
According to this resource, navigating Bering Strait is hard because of weather/geographical conditions and the legality of getting permission to leave Russia. From the linked source:
and (assume there are similar problem the other way)
A discussion on Lonely Planet's Thorn Tree forums mentions previous attempts and further information. A pertinent point is while it may be possible to cross, going on from there onwards to rest of Alaska/America has its own problems too.